Houston lawyer and businessman Mark White served as governor of Texas from 1983 to 1987 and as attorney general of Texas from 1979 to 1983. He co-chairs The Constitution Project’s Death Penalty Committee, a bipartisan group that promotes improvements in the death penalty system.

In 1990, when I was campaigning to take back the Texas governor’s mansion four years after I was unseated, I ran an ad I now regret. In it, I walked in front of blown-up photographs of 19 men who had been executed on my watch. “Only a governor can make executions happen,” I told the camera. “I did. And I will.”

I still believe that every one of those 19 men was guilty of a heinous crime and deserved to die. One had killed his son on Halloween in 1974 with cyanide-laced candy in order to claim $20,000 in life insurance. Another had repeatedly raped a minister’s wife before strangling her to death with a microphone cord.

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I also commuted other death sentences, usually on the recommendation of the local district attorney. I relied on my experience both as attorney general and as a lawyer in private practice to inform my judgments, and I spent hours poring over every case. The details of each were different, as were the reasons I let the execution orders stand, but none of the 19 who were executed ever proclaimed their innocence.

At that time, executions were conducted shortly after midnight, and on the night of each execution, I made sure I had a direct phone line to the death chamber in Huntsville so that if any last-minute issues arose, we could act. Oftentimes, I would walk outside the Capitol to speak to the protesters who assembled before each execution. Some called me a murderer, no better than the criminal who had just died. Others wanted to know why it took so long for justice to be served. Not only was I convinced of the guilt of each man, I would tell them, but I believed our criminal justice system delivered fair sentences and could humanely carry out the ultimate punishment.

Today, I’m not so sure. As I’ve watched how the death penalty has been administered over the years, both in Texas and around the country, it has become increasingly clear to me that we just don’t do a good job at any phase of the process, from ensuring that capital trials are fair to the actual handling of executions themselves. Anyone who watched with horror last week as Oklahoma botched the execution of Clayton Lockett—so badly that corrections officers drew the curtain so that the public didn’t have to watch the gruesome spectacle—would have to agree.

While I still believe that some crimes are so heinous that society is morally justified in demanding the perpetrator’s life be forfeited, we now have incontrovertible evidence that America’s criminal justice system does a poor job of determining who deserves the death penalty. Scores of people have been released from death row after evidence of their innocence emerged, including 12 from my home state of Texas. Particularly with the introduction of DNA testing, it has become increasingly clear that human error, even when prosecutors, judges and jurors all operate in good faith, is all too pervasive.

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And we now know with near certainty that innocent people have been put to death. For example, Texas in 2004 executed Cameron Todd Willingham, who was convicted of the murder of his three children by arson. Experts have now concluded that the original investigation in his case was seriously flawed and did not prove that that arson even took place. And just this year, it was discovered that Willingham’s prosecutor made a deal with a jailhouse informant in exchange for his testimony that Willingham had confessed the murder to him—a deal the prosecutor never disclosed to the defense at trial.

Similarly, DNA tests conducted in 2010, in conjunction with a key witness recanting his testimony, raised serious doubts that Texas death row inmate Claude Jones committed the murder for which he was convicted. Jones was executed in 2000.

While it’s impossible to know precisely how many innocent people face capital punishment today, a recent study by the National Academy of Sciences estimated that 4.1 percent of inmates sentenced to die are innocent. With more than 3,000 people on death row nationwide, even that conservative estimate means dozens are facing execution for crimes they didn’t commit.